Fully Analytic G₀W₀ Nuclear Gradients

In this letter, we present the first fully analytic derivation and implementation of nuclear gradients for the G₀W₀ method. For this, we leverage the recently established connection between the G₀W₀ approach and equation-of-motion unitary coupled-cluster theory for charged excitations. Analytic gradients are obtained through the Lagrangian technique and are implemented and validated by comparison with finite-difference calculations. For G₀W₀, we examine the effect of the Tamm-Dancoff approximation for evaluating the screened Coulomb interaction. Finally, we compare G₀W₀ adiabatic ionization potential and electron affinities to wave function-based electronic structure methods and experimental values.